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This method will use y = mx + b to find the equation instead of the point-slope method.
We are being asked to find the equation of a line perpendicular to -9x -2y = 10 that passes through the point (-9,9).
We will first find the slope of the perpendicular line by transforming the given equation into slope-intercept form which is y = mx + b.
-9x-2y = 10
-2y = 9x + 10
y = -9/2x - 5
The slope of a line perpendicular to the given equation will be 2/9 which is the "opposite reciprocal" of -9/2.
Now we will use direct substitution into y = mx +b to find the y intercept of the new equation.
y = mx + b
9 = 2/9(-9) + b
9 = -2 + b
Now, write the equation in slope-intercept form using the slope 2/9 and the y intercept 11.
The equation of the line that is perpendicular to the given line and containing the given point is y = (2/9)x + 11.
The slope-intercept form of the equation of a line is y = mx + c where m is the slope and c is the y-intercept.
The line given to us -9x - 2y = 10 can be written in the slope-intercept form as
-2y = 9y + 10
=> y = (-9/2)x - 5
The slope of the line is -9/2. As the product of the slope of two perpendicular lines is -1, the slope of the required line is 2/9.
The required line passes through (-9, 9). We get the equation:
(y - 9)/(x + 9) = 2/9
=> y - 9 = 2x/9 + 2*9/9
=> y = (2/9)x + 2 + 9
=> y = (2/9)x + 11
The equation of the required line is y = (2/9)x + 11
Write the slope-intercept equation for the line that passes through (-9, 9) and is perpendicular to -9x – 2y = 10 Please show all of your work.
-9x - 2y = 10
-9x - 10 + 2y
y = (-9/2)x - 5
The slope of this equation is -9/2. The slope of the perpendicular line is 2/9 (The negative reciprocal.
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